Download GTU B.Tech 2020 Winter 4th Sem 3141005 Signal And Systems Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER-IV (NEW) EXAMINATION - WINTER 2020

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Subject Code:3141005 Date:11/02/2021

Subject Name:Signal & Systems

Time:02:30 PM TO 04:30 PM Total Marks:56

Instructions:

1. Attempt any FOUR questions out of EIGHT questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Find even and odd parts of x(t) = u(t). 03

(b) Check whether the following system is dynamic, causal, time invariant, 04 stable: y[n] = 3 {x[n] + x[n — 1] + x[n — 2]}

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(c) Classify signals. Give examples of each. 07

Q.2 (a) Sketch the following waveform: x(t) = u(t + 1) — 2u(t) — 2u(t — 1). 03

(b) Define energy and power. Hence, define energy signal and power signal. 04

(c) Evaluate continuous time (CT) convolution integral given as: 07 y(t) = e^-2t u(t) * u(t +2)

Q.3 (a) Listout properties of convolution. 03

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(b) Find the step response of the system whose impulse response is given as: 04 h(t) = u(t+1) — u(t-1)

(c) Find the exponential Fourier series of Half wave rectifies sine wave shown 07 in figure:1.

Figure:1

Q.4 (a) Find the output of an LTI system with impulse response h(t) = d(t — 3) for 03 the input x(t) = cos 4t + cos 7t

(b) Calculate the convolution of x[n] and h[n]: 04 x[n] = {1,1,2,1,1} h[n] = {1,-2,-3,4}

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(c) Obtain the Fourier Transform of following signals: 07

1. x(t) = cos(?₀t)
2. x(t) = sin(?₀t) u(t)

Q.5 (a) State and prove frequency shifting property of Fourier Transform. 03

(b) Find the Fourier Transform of x[n] = —aⁿu[—n — 1] , where a is real. 04

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(c) Compute DFT of the following sequence x[n] = {0,1,2,3} 07

Q.6 (a) State and prove time scaling property of Fourier Transform. 03

(b) Bring out difference between DFT and Fourier Transform (FT). 04

(c) Find IDFT by calculating its DFT. 07

Q.7 (a) Prove time shifting property of z- transform. 03

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(b) What is ROC with respect to z- transform? What are its properties? 04

(c) Determine inverse z- transform of 07

X(z) = 1/(1-1.5z^-1+0.5z^-2) ,ROC: |z| >1

Q.8 (a) Prove differentiation in z-domain property of z- transform. 03

(b) Find the z- transform and ROC of the following sequence: 04 x[n] = d[n +1]+(1/3)ⁿ u[n] + 4ⁿu[—n — 1]

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(c) Determine the sequence x[n] from following function: 07

X (Z ) = (1+z^-1)/(1-z^-1+0.5z^-2) Assume that x[n] is causal.

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